Generalized URV subspace tracking LMS algorithm

The convergence rate of the Least Mean Squares (LMS) algorithm is poor whenever the adaptive filter input auto-correlation matrix is ill-conditioned. In this paper we propose a new LMS algorithm to alleviate this problem. It uses a data dependent signal transformation. The algorithm tracks the subspaces corresponding to clusters of eigenvalues of the auto-correlation matrix of the input to the adaptive filter, which have the same order of magnitude. The algorithm up-dates the projection of the tap weights of the adaptive filter onto each subspace using LMS algorithms with different step sizes. The technique also permits adaptation only in those subspaces, which contain strong signal components leading to a lower excess Mean Squared Error (MSE) as compared to traditional algorithms.